Stephanie is 28 years older than Jessica. For the last 3 years, Stephanie and Jessica have been going to the same school. Nine years ago, Stephanie was 5 times older than Jessica. How old is Stephanie now?
Solution: We can use the given information to write down two equations that describe the ages of Stephanie and Jessica. Let Stephanie's current age be $s$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $s = j + 28$ Nine years ago, Stephanie was $s - 9$ years old, and Jessica was $j - 9$ years old. The information in the second sentence can be expressed in the following equation: $s - 9 = 5(j - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = s - 28$ . Substituting this into our second equation, we get the equation: $s - 9 = 5($ $(s - 28)$ $ -$ $ 9)$ which combines the information about $s$ from both of our original equations. Simplifying the right side of this equation, we get: $s - 9 = 5s - 185$ Solving for $s$ , we get: $4 s = 176$ $s = 44$.